Let P and Q be two idempotents, we review the results about the equivalence between the
invertibility of a linear combination aP +bQ and that of P +Q, where a and b are any nonzero
complex numbers with a + b
eq 0. It is possible to extend the results to the case P and Q are
square-zero elements. However, we will show that these extensions are impossible in general
for P and Q being partial isometries or n-potents with n geq 3. We will show in case P and Q
are square-zero elements, the invertibility of P +Q is equivalent to that of aP +bQ for nonzero
a, b.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0709107-162359 |
| Date | 09 July 2007 |
| Creators | Wang, Chih-jen |
| Contributors | Jyh-Shyang Jeang, Hwa-Long Gau, Mu-Ming Wong, Mark C. Ho, Ngai-Ching Wong |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0709107-162359 |
| Rights | withheld, Copyright information available at source archive |
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